Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-29T19:50:38.395Z Has data issue: false hasContentIssue false
  • English
  • Français

A VECTOR BUNDLE OF RANK 2 ON ℙ1×ℙ3

Published online by Cambridge University Press:  01 June 1998

H. LANGE
H. LANGE
Affiliation:
Mathematisches Institut, Bismarckstrasse 1 1/2, D-91054 Erlangen, Germany
Get access

Abstract

It is well known that the Horrocks–Mumford bundle [Fscr ] encodes a lot of very interesting geometric information. This is essentially the reason for the fact that much work has been done in order to find other rank-2 bundles on ℙ4. The only nonsplit vector bundles of rank 2 on ℙ4, known up to now, are twists of pullbacks of [Fscr ] by finite coverings f[ratio ]ℙ4→ℙ4. So it seems to be a natural question to consider, instead of ℙ4, other Fano 4-folds. It is the aim of this note to give an example of a rank-2 vector bundle on ℙ1×ℙ3 and to show that it also admits very interesting geometric properties.

Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 57 , Issue 3 , June 1998 , pp. 583 - 598
Copyright
The London Mathematical Society 1998

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)